1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
alex41 [277]
3 years ago
7

Find the area ratio of a regular octahedron and a tetrahedron regular, knowing that the diagonal of the octahedron is equal to h

eight of the tetrahedron.
Mathematics
1 answer:
Anton [14]3 years ago
7 0

Answer:

\frac{4}{3}

Step-by-step explanation:

The area of a regular octahedron is given by:

area = 2\sqrt{3}\ *edge^2. Let a is the length of the edge (diagonal).

area = 2\sqrt{3}\ *a^2

Given that the diagonal of the octahedron is equal to height (h) of the tetrahedron i.e.

a = h, where h is the height of the tetrahedron and a is the diagonal of the octahedron. Let the edge of the tetrrahedron be e. To find the edge of the tetrahedron, we use:

h=\sqrt{\frac{2}{3} } e\\but\ h=a\\a=\sqrt{\frac{2}{3} } e\\e=\sqrt{\frac{3}{2} }a

The area of a tetrahedron is given by:

area = \sqrt{3}\ *edge^2 = \sqrt{3} *(\sqrt{\frac{3}{2} }a)^2=\frac{3}{2}\sqrt{3}    *a^2

The ratio of area of regular octahedron to area tetrahedron regular is given as:

Ratio = \frac{2\sqrt{3}\ *a^2}{\frac{3}{2} \sqrt{3}*a^2} =\frac{4}{3}

You might be interested in
HELP PLEASE!!!! What is the formula to this......dry beans, cereal, popcorn, rice, or other small grain (about 4 cups)  heavywe
topjm [15]

Answer:

9101

Step-by-step explanation:

do the math

3 0
3 years ago
What is 3x+4y=8 in slope intercept form?
Tpy6a [65]
Y=3/4x+2 cus u subtract than divide
3 0
3 years ago
Where would we find the point (–10,0)? A). y-axis B).quadrant ll C).x-axis D).quadrant lll
madreJ [45]
C because its not in any quadrant because the Y isn't stated so the point -10,0 is located on the X-axis
4 0
3 years ago
Read 2 more answers
How do you check the answer for the division problem eight divided by three hundred?
lawyer [7]

Answer:

you multiply the quotient times the divisor and your awnser should be the same as the dividend

Step-by-step explanation:

7 0
2 years ago
PLEASE ANSWER FAST
Lina20 [59]
The square root of 16 is 4
7 0
3 years ago
Read 2 more answers
Other questions:
  • It takes 45 minutes or 45 over 60 of an hour to cook a chicken? How many fourths of an hour is that?
    13·1 answer
  • 2/3 k =28•4/9 solve for k
    5·2 answers
  • When rope is selling at $.10 a foot, how many feet can you buy for sixty cents?
    9·2 answers
  • PLEASE HELP FIRST GETS BRAINLIEST.
    15·1 answer
  • there were twenty one adults in line at a movie theater.That is three times the number of children in line. how many children we
    5·1 answer
  • Which factorization is equivalent to 4y2 − 17y + 15?
    6·1 answer
  • Yesterdays low temperature was -2.5°C today low temperature is five times as lone as yesterday’s low temperature
    8·1 answer
  • Please answer this question now
    6·1 answer
  • Ian'sbirthdaypartycosts
    13·1 answer
  • F(x) = 4(x + 3)2 , x > 0
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!